Senior officials said that U.S. law enforcement has run the list of U.S. persons named on Twitter as involved in the Kenya mall attack against the list of U.S. persons known to be affiliated with al-Shabaab. They have found no match at this time.

Officials said it may be possible the Twitter information was false, the names given were aliases or the U.S. government did not know about them.

"At this point, we have no definitive evidence of the nationalities or identities of the perpetrators," said State Department spokeswoman Jen Psaki at a Monday afternoon briefing.

However, CNN said it had not confirmed any American involvement with the jihadists, though numerous organizations were looking into the claims.

Three attackers were killed in the fighting Monday, officials said, and more than 10 suspects arrested. Eleven Kenyan soldiers were wounded in the running gun battles. By evening, Kenyan security officials claimed the upper hand.

"Taken control of all the floors. We're not here to feed the attackers with pastries but to finish and punish them," Police Inspector General David Kimaiyo said on Twitter.

Kenya's interior minister said the evacuation of hostages "has gone very, very well" and that Kenyan officials are "very certain" that there are few if any hostages left in the building.